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\begin{equation*}\sin \frac{11 \pi}{60} = \sin 33^\circ = \frac{2 \sqrt{5 + \sqrt 5} \left( -1 + \sqrt 3 \right) + \sqrt 2 \left( \sqrt 5 - 1 \right) \left( 1 + \sqrt 3 \right)}{16}\end{equation*}
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